One of the major problems of the mathematical theory of systems with self-organization is to understand how global phenomena emerge from local interactions between agents. In the context of alignment dynamics such questions were addressed already in the seminal works of Cucker and Smale [1]}, [2]} and studied extensively in [3]}, [4]}, [5]}, [6]}, [7]}. Two underlying mechanisms lie behind rigorous results in this direction – either sufficiently strong communication at long range to ensure that no agent escapes the influence of the crowd, or perpetual connectivity of the flock at local communication range which ensures exchange of information between agents at all times.
